Now, we’ll build upon the previous risk model by including two additional factors for a total of three. This is the famous Fama-French model, which can be considered the model that started the movement towards multi-factor models. The original three-factor Fama-French model includes the market return, and adds two additional factors, which the other’s called size and value. Let’s look at these two additional factors, and how the data for them are generated. The first additional factor we will look at is size. The size of a company is measured by its market cap. There’s been evidence that shows, that small-cap companies have higher average returns compared to large-cap companies. In other words, if we can determine that company ABC is a small-cap stock, valued at one billion dollars, and company XYZ, is a large cap stock valued at $10 billion, then we could expect that company ABC will have higher risk adjusted returns, compared to XYZ. The question is how much more return can we expect for company ABC for being a fraction of the size of XYZ? Remember that we’re trying to fill in the factor risk model. The factor covariance matrix uses the time series of factor returns for the three factors: market, size and value. Well, if you had evidence, that small cap stocks had higher than average returns, than large-cap stocks, what would you do as a rational investor to make use of this knowledge? One way that seems to make sense is to buy small-cap stocks, and to short large-cap stocks. If we had a portfolio in which you bought small-cap stocks and shorted large-cap stocks, we could track the portfolio’s value over time so we’d have a time series. We could also calculate the daily return on this portfolio. The return of this portfolio is the return of the size factor. Let’s think about what this portfolio tells us. If the portfolio’s return is positive, it means that on that day, favoring small cap stocks had a positive effect on the portfolio’s return. If the portfolio’s return is negative, then it means that on that day, favoring small cap stocks had a negative effect on the portfolio’s return. So that’s pretty cool. We have a way of quantifying whether a smaller size actually adds to positive or negative returns on each day.